Ch 17: Actuarial funding

Question 1

Initial charges and NUB strain on UL policies

5

Answer 1

• Hold reserve to cover initial expenses = normal reserve - EPV(initial expense charge)
• Alloc Prem= units
• Unalloc Prem= NUF=> initial charges paid from
• High initial costs are funded by the the change in alloc % in early years
  
  • Decr NUB strain hold a neg non-unit reserve
  • NO longer PRE

Question 2

What is the aim of actuarial funding? (4)

Answer 2

1. Hold lower reserves for UL contracts @ inception to reduce NUB strain
2. Actuarial funding is when the insurer takes credit for some of the extra future annual management charges in present day’s terms.
3. Money saved can be used to cover initial expenses.
4. Missing unit funds then bought later on from future management charges and management charge should thus be greater than the actual fund management expenses.

Take credit @ inception by alloc less money to PH unit account in early years

Question 3

What are the requirements necessary for actuarial funding to work? (5)

Answer 3

1. Permitted by regs
2. Benefit contingent on death/survival
   
   • ​for minimum period of years, thus still some risk on death
3. Unit related charge
   
   • company hold less than full funded value
   • additional units purchased over lifetime (using unit related charges)
   • unit charge exactly sufficient (because charge is unit related, irrespective of any price movement)
4. Sufficient regular fund management charges
   
   • ​limiting condition is that after actuarial funding, prudently projected future net cashflow to insurer remain positive
   • shortfall capitalised in non-unit reserve
5. Unit-linked related surrender penalty
   
   • ​imposed such that unit reserve not lower than surrender value payabl

Question 4

What common mechanisms can be used to implement actuarial funding? (2)

Answer 4

Req charging structure that has incr level of management charges

1. Higher fund managment charges
   
   • on all units
   • need sizeable quanity of fund management charges to pre fund
2. Capital/accumulation units (with different management charges)
   
   • capital units: attracts higher managment charge, typically allocated premiums used to buy these during first few years
   • accumulation units: lower management charge, allocated premiums used to buy later on
   • however, has issues with transparency:
     
     • thus no longer really used in contract design
     • but because of long term nature, still many policies in force

Question 5

Actuarial funding factors

Answer 5

• Unit fund is fully funded
  
  • Units held=bid val purch by alloc prems
  • Only req when contingent event occurs
• Liabilities are contingent so hold EPV of unit fundand not fully funded value
• For endowment assurance at policy duration t allowing for contingency of death would be (using a suitably chosen basis):
• EPV(ULEA)t = (UF)_t * A_(x+t:n-t), where
  
  • UF_t is the fully funded value of the unit fund at policy duration t
  • x is the entry age
  • n is the policy term
  • A_{(x+t:n-t) is the actuarial funding factor}
• Discount rate used should be
  
  • proportion of fund management charge we wish to take advance credit for
  • consider the ability to cover renewal expenses using man charge

Question 6

What is the effect of actuarial funding on net cashflows from the unit fund? (5)

Answer 6

1. Increases cashflows to non-unit fund (funding factor)
   
   • (UF)0 * (1-Ax:n) can be trans to non-unit fund
   • Decr NUB strain due to high expenses
2. Reduced future managment charges transferred
   
   • transferred from unit fund to non-unit fund,
   • charge is only levied on actual number of units purchase (which will now be less)
3. Additional charges/reduced credits
   
   • to non-unit fund will be much smaller than the additional credit as result of actuarial funding,
   • providing charge on units is large enough
4. Creates additional liability on non-unit fund
   
   • (Guar Ben - bid val units) is now larger as bid val is smaller
   • this expected additional death cost is a charge on non-unit fund at each year end
5. Swap high future managment charges for capitalsed sum early
   
   • thus matched cashflows from policy with incidence of expenses

Question 7

Considerations when applying actuarial funding? (2)

Answer 7

1. Don’t allow excess management charges on the calculation of non-unit reserves
   
   • only residual cashflows from unit fund can be counted towards future cashflow projections
   • full fund management charge is no longer available for this purpose
2. Unit fund held should not be less than surrender value
   
   • thus, extent actuarial funding used is restricted by amount of any surrender penalty (reduction in benefit from bid value of units)
   • too risky to deduct cost of additional benefit on surrender, coz surrender is policy option, it is quite feasible for all policies to surrender over a very short period of time.
   • would then have to find value of units almost immediately, and there’d be inadequate reserves

Question 8

Advantages of actuarial funding? (7)

Answer 8

1. Lower reserves
2. Reduce new business strain
3. Write more new business
4. More capital efficient
   
   • Charges/expenses well-matched
5. allows initial allocation (insted of zero allocation to match charges/expenses)
   
   • making product more marketable than if allocation was zero
6. Reduced investment/persistency risk
   
   • because charges/expenses more closely matched

Question 9

Disdvantages of actuarial funding? (5)

Answer 9

1. Regulatory restrictions
2. Can be complicated
   
   • particularly when used together with capital units
3. Issues because of complexity
   
   • reduced transparency
   • poor persistency because of selling to clients who don’t understand
   • restricts distribution channels
   • more effort required to sell
   • may restrict level of sales, depending on remuneration
4. Requires surrender penalty
   
   • which may be unattractive
5. Increase mortality risk
   
   • As sum at risk will be higher due to greater discrepency between reserves held and face value of units

Question 10

Summary

Answer 10

• Flows from unit fund to non-unit fund
• Actuarially funded units cashflow of unit management charges from the unit fund to the non-unit fund will be adjusted. Calculated by (for first two points):
  
  • UF_(t-1) * F_(t-1) * (1+g) - UF_(t) * F_(t)
  • where UF_(.) is the face value of units at .
  • F_(.) is the actuarial funding factor at .
  • g is the unit growth over the year
• difference between fully and actuarially funded units
  
  • cashflow from unit fund to non-unit fund on each unit purchased
• charge on units
  
  • cashflow from unit fund to non-unit fund, followed at same time by cashflow from non-unit fund to unit fund to build up inreasing number of actuarially funded capital units required at year-end
• excess of value of units (actually held by company over surrender value granted)
• Flows from non-unit fund to unit fund
  
  • cost of excess guaranteed minimum sum assured on death
    
    • over the value of units actuallyp held by company